1. Lesson 4

1.7. Explore 3

Mathematics 30-1 Module 8

Module 8: Permutations, Combinations, and the Binomial Theorem

 

In Lesson 3 you looked at combinations. Do you think there could be a connection between combinations and Pascal’s triangle? In Try This 3 you will explore whether there is a relationship between combinations and Pascal’s triangle.

 

Try This 3
  1. Consider the following table of combinations and their values.

    TABLE OF COMBINATIONS

    Combination

    Value

    0C0

    1

    1C0

    1

    1C1

    1

    2C0

    1

    2C1

    2

    2C2

    1

    3C0

    1

    3C1

    3

    3C2

    3

    3C3

    1

    4C0

    1

    4C1

    4

    4C2

    6

    4C3

    4

    4C4

    1
    1. Describe a relationship between the table of combinations and Pascal’s triangle.

       
      This image shows the first 8 rows of Pascal’s triangle.
    2. Try your relationship for row 7.
    3. Use your relationship to predict the 1st, 2nd, 3rd, and 4th numbers of row 34 of Pascal’s triangle.
    4. Determine the first four terms of (x + y)33.
  2. Explain a general method that can be used to predict the terms of the expansion of (x + y)n.

course folder Save your responses in your course folder.

 

Share 3

 

With a partner or group, discuss the following question based on the information in Try This 3.

 

Compare the strategies you thought of to determine the terms of the expansion of (x + y)n.

 

course folder If required, save a record of your discussion in your course folder.

Use the exponent pattern you learned earlier.